-LRB- CNN -RRB- -- Journalist Bob Woodward describes in his new book a secret U.S. program to assassinate terrorists in Iraq .

CNN 's Michael Ware says , `` The U.S. subcontracted out an assassination program against al Qaeda ... in early 2006 . ''

Woodward , an associate editor of The Washington Post , says in `` The War Within : A Secret White House History 2006-2008 '' that the assassination program , not the 2007 increase in U.S. forces in the war zone known as `` the surge , '' is primarily responsible for the reduction of violence in Iraq .

CNN Baghdad correspondent Michael Ware cast doubt on Woodward 's assertion Tuesday in a conversation with `` American Morning '' host John Roberts . Watch Larry King on his talk with Woodward ''

John Roberts : What do you think of what Woodward is saying ?

Michael Ware : Let 's say that these `` fusion teams , '' as they 're being called , have come into effect . The first thing to say is , `` Well , about time . ''

On the ground you 've seen the lack of coordination as the left hand of one agency is not with the right hand of another agency within the American effort . But by and large , to suggest that anything like this being done now has been the major reason for the decline in violence is a bit rich .

I mean , the U.S. subcontracted out an assassination program against al Qaeda way back in early 2006 . And this was conceded by the then-chief of military intelligence in Baghdad and by -LSB- U.S. -RSB- Ambassador Zalmay Khalilzad himself . That 's what broke the back of al Qaeda .

Then when America put 100,000-plus insurgents on the U.S. government payroll , including members of al Qaeda , that not only took them out of the field , but it also let them run their own assassination programs against the Iranian-backed militias .

Roberts : So it sounds like assassination was a real part of the program here , but was that the only thing that worked ? What about the addition of these troops and these neighborhood stations that were set up ? Did it all kind of work together ?

Ware : It does work together . But the key to the downturn in violence that we 're seeing now is not so much the surge of 30,000 troops in itself .

What it 's been is the segregation of Baghdad into these enclaves . It 's been cutting a deal with Muqtada al-Sadr , the leader of the Iranian-backed militia . And primarily it 's been putting your enemy on your payroll -- the Sunni insurgents and many members of al Qaeda . That 's what 's brought down the violence . This is your American militia , the counterbalance to the Iranian militias .

So if there 's new teams out there with new technology , great . But they 're riding the wave of previous success .

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Bob Woodward credits assassination teams in large part for lower violence in Iraq

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CNN Baghdad correspondent Michael Ware says that 's not all of it

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Co-opting of insurgents and al Qaeda in Iraq had bigger impact , Ware says

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Deal with Muqtada al-Sadr , leader of Iranian-backed militia , also key , Ware says